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How can you tell if two equations for parallel lines or perpendicular lines. please explain?

Example: x+y+7 x-y=3 are those parallel or perpendicular or none

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To find out if they are parallel we need to see if the gradient is the same, to do this we need to get y in terms of x:assuming the first equation is x+y+7=0y=-x-7andy=x-3The gradient is the coefficient of x (the number infront of x)For equation 1 the gradient is -1, and for number 2 it is 1, therefore they are not parallel.However to check if they are perpendicular we need to see if their gradients multiply to equal -1.-1*1=-1 therefore they are perpendicular